(C) The potential energy stored in a capacitor is given by $U = \frac{1}{2} CV^2$.Since the battery remains connected,the potential difference $V$ acr

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Assertion is true but the reason is false.

(C) The potential energy stored in a capacitor is given by $U = \frac{1}{2} CV^2$.Since the battery remains connected,the potential difference $V$ across the plates remains constant.Therefore,$U \propto C$.When a dielectric material is inserted,the capacitance $C$ increases $(C = K C_0)$.As $C$ increases,the potential energy $U$ also increases.Thus,the assertion is true.However,when the battery remains connected,the charge $Q = CV$ changes because $C$ changes while $V$ remains constant.Therefore,the reason is false.

Class 12 Physics Electric Potential and Capacitance Effect of Dielectric Inside Capacitor

Medium

Assertion: When a battery remains connected,the electric potential energy increases if a dielectric material is inserted between the plates of a capacitor.
Reason: When a battery remains connected,the charge on the plates of the capacitor remains the same.

A
Both assertion & reason are true & the reason is a correct explanation of the assertion.
B
Both assertion & reason are true but reason is not a correct explanation of the assertion.
C
Assertion is true but the reason is false.
D
Both assertion & reason are false.

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Class 12

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Electric Potential and Capacitance

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Effect of Dielectric Inside Capacitor

Consider the arrangement shown in the figure. The total energy stored is $U_1$ when the key $K$ is closed. Now,the key $K$ is opened,and two dielectric slabs of relative permittivity $\epsilon_r$ are introduced between the plates of the two capacitors. The slabs fit tightly between the plates. The total energy stored is now $U_2$. Then,the ratio $U_1/U_2$ is:

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Two capacitors $C_1$ and $C_2$ are connected to a battery as shown in the figure. The space between the plates of $C_1$ is filled with air,and the space between the plates of $C_2$ is filled with a dielectric material. Which of the following is true regarding the charges $Q_1$ and $Q_2$ on the capacitors?

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$A$ parallel plate capacitor with air between the plates has a capacitance of $4 \ pF$. If the distance between the plates is reduced by half and the space between them is filled with a substance of dielectric constant $K = 6$,then the value of capacitance will be . . . . . . . (in $pF$)

EasyGUJCET 2024

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$A$ parallel plate capacitor has a separation between plates of $0.885$ mm. It has a capacitance of $1$ $\mu$$F$ when the space between the plates is filled with an insulating material of resistivity $1 \times 10^{13}$ $\Omega$m and resistance $17.7 \times 10^{14}$ $\Omega$. The relative permittivity of the insulating material is $\alpha \times 10^7$. The value of $\alpha$ is . . . . . . . (Take permittivity of free space $\epsilon_0 = 8.85 \times 10^{-12}$ $F$/m)

DifficultJEE MAIN 2026

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$A$ capacitor of $10 \mu F$ capacitance,whose plates are separated by $10 \text{ mm}$ through air and each plate has an area of $4 \text{ cm}^2$,is now filled equally with two dielectric media of $K_1=2$ and $K_2=3$ respectively,as shown in the figure. If the new force between the plates is $8 \text{ N}$,the supply voltage is . . . . . . $V$.

DifficultJEE MAIN 2024

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Assertion: When a battery remains connected,the electric potential energy increases if a dielectric material is inserted between the plates of a capacitor.Reason: When a battery remains connected,the charge on the plates of the capacitor remains the same.

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$A$ parallel plate capacitor with air between the plates has a capacitance of $4 \ pF$. If the distance between the plates is reduced by half and the space between them is filled with a substance of dielectric constant $K = 6$,then the value of capacitance will be . . . . . . . (in $pF$)

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Assertion: When a battery remains connected,the electric potential energy increases if a dielectric material is inserted between the plates of a capacitor.
Reason: When a battery remains connected,the charge on the plates of the capacitor remains the same.